family, community and long-term earnings inequalityftp.iza.org › dp10089.pdf · discussion paper...
Post on 30-Jun-2020
1 Views
Preview:
TRANSCRIPT
Forschungsinstitut zur Zukunft der ArbeitInstitute for the Study of Labor
DI
SC
US
SI
ON
P
AP
ER
S
ER
IE
S
Family, Community and Long-Term Earnings Inequality
IZA DP No. 10089
July 2016
Paul BingleyLorenzo CappellariKonstantinos Tatsiramos
Family, Community and
Long-Term Earnings Inequality
Paul Bingley SFI Copenhagen
Lorenzo Cappellari
Università Cattolica Milano and IZA
Konstantinos Tatsiramos
University of Nottingham and IZA
Discussion Paper No. 10089 July 2016
IZA
P.O. Box 7240 53072 Bonn
Germany
Phone: +49-228-3894-0 Fax: +49-228-3894-180
E-mail: iza@iza.org
Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author.
IZA Discussion Paper No. 10089 July 2016
ABSTRACT
Family, Community and Long-Term Earnings Inequality* This paper studies the influence of family, schools and neighborhoods on life-cycle earnings inequality. We develop an earnings dynamics model linking brothers, schoolmates and teenage parish neighbors using population register data for Denmark. We exploit differences in the timing of family mobility and the partial overlap of schools and neighborhoods to separately identify sorting from community and family effects. We find that family is far more important than community in influencing earnings inequality over the life cycle. Neighborhoods and schools influence earnings only early in the working life and this influence falls rapidly and becomes negligible after age 30. JEL Classification: D31, J62 Keywords: sibling correlations, neighborhoods, schools, life-cycle earnings, inequality Corresponding author: Lorenzo Cappellari Department of Economics and Finance Università Cattolica Milano Largo Gemelli 1 20123 Milano Italy E-mail: lorenzo.cappellari@unicatt.it
* We thank Anders Björklund, Stephen Gibbons, Markus Jännti, Bash Mazumder, Andreas Peichl, Josef Zweimüller, seminar audiences at IZA in Bonn, SOFI in Stockholm, Lund University, Paris School of Economics, JRC in Ispra, University of Padua, University of Venice, ZEW in Mannheim, European University Institute in Florence, IAB in Nuremberg, and conferences audiences at Royal Economic Society in Manchester, European Society of Population Economics in Braga, 16th IZA/CEPR European Symposium in Labour Economics (ESSLE), Fourth SOLE/EALE World Conference in Montreal, DynIPer in Marseille and the Intergenerational Mobility workshop in Madrid for their comments. The usual disclaimer applies. The research for this paper was supported by a British Academy Research Grant (award no. SG113192) and by Danish Strategic Research Council Grants (codes DSF-09-070295 and DSF-10- 093105).
1
1. Introduction
That the environment in which persons grow up and live in the early stages of their life is an
important determinant of lifetime socioeconomic outcomes has been well established in the recent
economic literature. Francesconi and Heckman (2016) report that at least 50% of the variability of
lifetime earnings across persons is due to differences in attributes determined by age 18. Family
and community background, which includes the neighborhood where children grow up and the
school they attend, are considered important attributes determining later outcomes (e.g. Page and
Solon, 2003; Raaum, Sørensen and Salvanes, 2006; Chetty and Hendren, 2015). Families can
determine earnings by transmitting abilities, preference and resources, while communities can
influence earnings through neighborhood quality, school quality and peers.
In this paper, we study the relative influence of family, schools and neighborhoods on
earnings inequality over the life cycle. While there is a large and growing body of evidence on the
influence of each of these attributes on adult outcomes, very little is known about their relative
influence on earnings and how it evolves over the life cycle. Understanding the relative magnitude
of these initial conditions on earnings throughout the life cycle is important for identifying the
driving forces of existing inequalities and for interventions that aim to reduce them, especially
because some early influences may be longer lasting than others.
There are two important challenges to consider in this analysis. The first challenge is
related to data availability, since tracing the relative influence of these attributes on earnings over
the life cycle requires almost complete earnings trajectories. We address this first challenge by
using data from administrative registers of the Danish population, which due to their longitudinal
dimension allow us to create individual earning histories based on tax records up to age 51 and
avoid the well-known measurement error and life cycle biases. Long earnings histories enable us
to assess the importance of families and communities in shaping the inequality of permanent
2
earnings, which are generally considered to be the most relevant for individual welfare because
transitory earnings shocks are more insurable (Blundell, Pistaferri and Preston, 2008).
The second challenge is that families with better resources or abilities tend to select better
schools and neighborhoods. Because of sorting, separating the influences of family and
community requires variation of the community environment that is exogenous to the outcome.
We address this second challenge by observing siblings, their schoolmates and their close
neighbors – sharing the same parish of residence – in the year they turn 15, which is the last year
of compulsory education in Denmark.1 In our research design, since communities are defined on
the basis of individual year of birth, siblings can be exposed to different communities (school,
neighborhood or both) because of family mobility in the time window between the years each
sibling turns 15. Specifically, variation in community exposure is coming from families who move
after the year the older sibling turns 15 and before the year the younger sibling turns 15, so they do
not reside in the same community at age 15. This variation in community exposure due to family
mobility within a specific time window allows separating community effects from family effects.2
However, it could be argued that this variation in community exposure may be subject to
selection due to underlying unobserved differences between moving and staying families, where
the latter are families for which siblings are in the same community at age 15. To support the
validity of the identifying assumption we also exploit plausibly exogenous variation in community
exposure coming from differences in the timing of mobility among only moving families. These
are all families who move, so it is only the difference in the timing of mobility that exposes
siblings to different environments. In this case, the comparison is between families who move after
1 By defining community exposure at a specific age we consider closer neighbors and schoolmates since, all else equal, peers of the same age are more likely to interact than peers of different ages. In sensitivity checks we show robustness to defining neighborhood exposure at a specific age down to age 10. 2 In the analysis we consider only males by sampling brother pairs, their male neighbors and male schoolmates. As we discuss in detail in Section 3, in our sample each male aged 15 has on average 19.5 male schoolmates born in the same year, and 14.6 male neighbors living in the same parish born in the same year.
3
the year the older sibling turns 15 – inducing within-family variation in community exposure – and
families who move after the older sibling turns 10 but before turning 15 – so both siblings are in
the same community at age 15. We can also separate neighborhood from school effects because in
Denmark an important institutional feature is that public school catchment areas do not completely
overlap with parishes. This implies that neighbors may be enrolled in different schools and
schoolmates may come from different parishes.3
For estimation, we exploit the linked earnings records of siblings, neighbors and
schoolmates and develop a model of individual earnings dynamics in the spirit of Baker and Solon
(2003), which we extend to account for the joint earnings dynamics of multiple groups of
individuals.4 We consider time series of individual earnings from age 24 and up to age 51. Our
model features life-cycle profiles, representing the long-term or permanent component of earnings,
and transitory shocks. We allow the inequality of long-term earnings to depend on inequality in
initial earnings, which reflects heterogeneous human capital investments, and inequality in
earnings growth rates, capturing heterogeneous returns to investments. We allow these two sources
of inequality in long-term earnings to depend on heterogeneity among families and heterogeneity
among youth communities, consistent with the idea that, by affecting human capital investments
and their returns, circumstances early in life may have long lasting effects. We also allow for
purely idiosyncratic unit root shocks over the life cycle which permanently shift individual
earnings trajectories. We use the estimated parameters of the model to decompose for the first time
the sibling correlation of earnings into the three components of interest – family, neighborhood
and school – allowing for life cycle dynamics.
3 Among schools 89.5 percent have individuals from more than one parish, and amongst parishes 60.1 percent have individuals from more than one school. See Section 3 for details. 4 Bingley and Cappellari (2013) extended Baker and Solon (2003) to account for dynamics within a three-person family, i.e. three pairwise relationships. With respect to Bingley and Cappellari (2013) we account for dynamics within three groups (family, school and neighborhood), i.e. three types of relationships, but each type of relationship could have arbitrarily many pairwise relationships, depending on how many individuals belong to each group.
4
We find that family is far more important than community in influencing earnings
inequality over the life cycle. There is an almost equal positive influence of neighborhoods and
schools on earnings only early in the working life, which falls rapidly becoming insignificant after
age 30. This implies that measuring earnings at relatively young ages leads to overstate the long
term relevance of community effects. In particular, the share of sibling correlation accounted for
by community effects is 27 percent if incomes are measured up to age 25, it drops to 19 percent if
incomes are measured up to age 30, but it is only 6 percent if we consider the entire available life
cycle profile of earnings up to age 49. This implies on average over the life cycle a limited
influence of community background because any community effects early in life are not long
lasting. These findings highlight the importance of considering the long-term effects of community
background on earnings beyond the first years of the working life. These results are robust to the
definition of youth communities, the degree of exposure to communities and various sample
selection choices.
Generally speaking, this paper contributes to the literature on the influence of family and
community background on earnings. The correlation of sibling earnings, which measures the
fraction of the variation in permanent earnings that can be attributed to both observed and
unobserved factors shared by siblings during childhood, has been widely used as an omnibus
measure of the influence of both family and community background (for reviews see Solon, 1999;
Björklund and Jännti, 2009; Black and Devereux, 2011). To disentangle family from community
effects, a common approach followed in this literature is to compare the correlation of sibling
earnings with the correlation of earnings among unrelated neighbors (e.g. Page and Solon, 2003;
Raaum, Sørensen and Salvanes, 2006). The idea is that while siblings share both the family and
the neighborhood, unrelated neighbors share only the neighborhood but not the family. The
findings from this approach suggest a substantial effect of neighborhoods on earnings. However,
5
the estimated neighborhood effect is recognized to be an upper bound because of non-random
sorting of families into neighborhoods, which leads to a positive correlation between the two
factors. Dealing with sorting by exploiting quasi-random assignment of families to public housing
projects in Toronto, Oreopoulos (2003) finds a zero influence of neighborhood quality in the total
variance of income and wages.
We contribute to this literature by developing a unified framework that allows us to
measure the relative influence of family and community background on earnings over the life
cycle, and also by distinguishing between the influence of neighborhoods and schools. The key
difference between our research design and the one common in the sibling correlation literature is
that, by defining communities on the basis of individual year of birth, we can separately identify
sorting from neighborhood, school and family effects by exploiting arguably exogenous family
mobility across communities and the partial overlap of schools and neighborhoods. We show that
without exploiting the variation in community exposure that allows identifying sorting, the
influence of neighborhoods and schools are found to be persistent throughout the life cycle and
upward biased by a factor of three. This highlights the importance of sorting and also that, despite
Denmark being generally considered a more equitable society, there are still important community
differences that families tend to react to similarly to other countries.
Outside the sibling correlation literature, this paper relates to the large and growing
literature on the impact of neighborhoods on children and adult outcomes. The evidence from
social experiments such as the Moving to Opportunity program (MTO), in which families living in
high poverty neighborhoods in five U.S. cities were randomly assigned vouchers to move to less
impoverished neighborhoods, suggests that changes in neighborhood quality had on average little
impact on economic outcomes (e.g. Ludwig et al., 2013). Recently, Chetty, Hendren and Katz
(2016) complement MTO data with administrative information from tax returns and find that
6
moving to a higher income neighborhood is associated with increased earnings in the mid-twenties
for children who were below age 13 when their families moved. Using tax records for the general
U.S. population, Chetty and Hendren (2015) exploit differences in the timing of mobility during
childhood to show that moving to a better neighborhood has positive effects on earnings during
early adulthood up to age 30, and the effect is greater with longer childhood exposure.
In our study, we exploit variation in community exposure for Denmark – due to differences
in the timing of mobility – which is similar to the variation exploited by Chetty and Hendren
(2015) for the U.S. We find similar positive youth neighborhood effects on earnings during early
adulthood and up to age 30, but these effects are not persistent later in the working life. This
evidence of no effects in the very long run is consistent with the evidence by Gould, Lavy and
Paserman (2011) who use the airlift of Yemenite immigrants as a natural experiment and find that
there are no very long run effects of early childhood environment on economic outcomes.5
Finally, this paper relates to the literature on the effect of school quality and peers on
earnings. Early studies measuring school quality with the pupil/teacher ratio report a positive
effect on the rate of return to schooling and earnings (Card and Krueger, 1992) whereas others find
no impact at all (Dearden, Ferri and Meghir, 2002). More recently the focus has shifted to long run
earnings. Black, Devereux and Salvanes (2013) correlate characteristics of 9th grade Norwegian
schoolmates with outcomes at age 33-44 and find a strong relation between focal pupil earnings
and peer fathers’ earnings. Another branch of this literature exploits (quasi-) random variation of
class size with most studies finding no effects (Leuven and Kokken, 2015; Falch, Strom and
Sandsor, 2015 for Norway, Chetty et al., 2011 for the US), while Fredriksson, Öckert and
Oosterbeek (2013) find a significant (at the 10 percent level) effect of smaller classes on long-term
5 Studies focusing on educational achievement outside the sibling correlation framework but using quasi-experimental variation of neighborhood quality have also found no impact of neighborhoods (e.g. Jacob, 2004; Gibbons, Silva and Weinhardt, 2013).
7
earnings. In summary, long run school effects on earnings are often found to be zero or borderline
significant. In our study, we measure the long-term effects of any school attribute shared between
schoolmates, finding – similar to neighborhood effects – a positive effect on earnings only in the
beginning of the working life and not in the very long run.
The paper is structured as follows. In Section 2 we develop the econometric model based
on the joint analysis of life-cycle earnings for brothers, neighbors and schoolmates. In Section 3
we describe the data and contrast our neighborhood definition with that used in comparable
studies. In Section 4 we present descriptive statistics on earnings of siblings and peers over the life
cycle. In Section 5 we present the main results comparing our findings to the previous literature,
robustness to the identification assumption and detailed sensitivity analysis. We conclude in the
last section.
2. Econometric Model
The aim of this paper is to identify the determinants of long-term earnings and, in particular, the
extent to which earnings inequality can be explained by differences in family and social
background. To estimate the contributions of family and community background on permanent
earnings we exploit the linked earnings records of siblings, teenage neighbors and schoolmates
within a model of multi-person earnings dynamics, distinguishing permanent from transitory
earnings and allowing for heterogeneous earnings growth.
We separate life cycle effects from calendar time trends by considering the distribution of
earnings within two-year birth cohorts. In particular, the residual log earnings – after regressing
log real gross annual earnings on year dummies and a quadratic age trend by birth cohort group –
denoted by w, are assumed to be the sum of two components, which are orthogonal by definition:
(i) a permanent component denoted by y and (ii) a transitory component denoted by v,
8
������ = ������ + ����� ; ������������� = 0, (1)
where the indices i, f, s, n and a stand for individual, family, school, neighborhood and age,
respectively.6 Schools and neighborhoods are defined as the school attended at age 15 and the
parish of residence at age 15. In Section 3 we provide details on sample construction and
community definition.
The model extends the joint earnings dynamics model of Bingley and Cappellari (2013) for
three persons (a father and two sons) to several multi-person groups. The model also tackles the
two measurement error biases in the estimation of correlations in permanent earnings between
persons which are highlighted in the literature of earnings correlation between family members,
particularly fathers and sons. The first source of bias addressed by the model is related to
transitory income shocks, which make current earnings a poor measure of permanent earnings
(Solon, 1992; Mazumder, 2005). Separate identification of permanent and transitory earnings is
granted by the availability of individual level panel data. The second source of bias addressed by
the model is related to life-cycle bias due to age differences between family members and the
heterogeneous earnings variation over individual life cycles (Jenkins, 1997; Haider and Solon,
2006; Bohlmark and Lindquist, 2006; Nybom and Stuhler, 2016).
2.1 Specification of permanent earnings
We allow permanent earnings (y) in equation (1) to depend on both shared and idiosyncratic
components. Shared components capture those determinants of permanent earnings that are
common between siblings, schoolmates and neighbors. The idiosyncratic component represents
individual-specific sources of variation in permanent earnings. We model life-cycle dynamics of
shared components using a specification based on heterogeneous income profiles (HIP), which is
6 Age is measured in deviation from the life cycle starting point, which is set at 24.
9
also known as a random growth model. We augment this with a restricted income profile (RIP)
process for individual-specific components, which is an idiosyncratic unit root (random walk)
shock.
The heterogeneous income profile specification is inspired by human capital models in
which heterogeneity of initial earnings and heterogeneous earnings growth are generated by
differential investments (Mincer, 1958; Ben-Porath, 1967). Based on the analysis of Becker and
Tomes (1979), parents can influence the human capital of their offspring by transmitting abilities,
preferences and resources, and thereby affect offspring earnings. Community background can also
influence individual outcomes through institutions such as the school and its quality (e.g.
Hanushek, 2006), or through the quality of neighborhood, or peer influences, social norms and role
models in the neighborhood (e.g. Wilson, 1987).
Differences between families in the availability of these traits, resources and exposure to the
community environment would lead to differences in human capital accumulation. Human capital
models predict that heterogeneous investments in human capital induce an inverse relationship
between initial earnings and earnings growth rates, because investors trade off initial earnings
against earnings growth throughout the life cycle. The resulting negative covariance of initial
earnings and growth rates would generate a U-shaped evolution of earnings dispersion by age due
to the ‘Mincerian cross-overs’ of earnings profiles. These observations motivate our specification
choice for shared earnings determinants, which reflects the idea that the across persons
resemblance of earnings stems from similarities in social background and human capital
investments. We show in Section 4 that the life-cycle patterns of earnings correlations between
siblings and peers are consistent with these mechanisms.
Besides the earnings profile shared by siblings, neighbors and schoolmates, we assume
permanent earnings to follow a restricted income profile, which is modeled as a unit root in age
10
( ��� ) and captures long-term individual deviations from the shared profile. This represents
idiosyncratic ability revealed over time, either to the labor market or to individuals themselves.
Overall, our permanent earnings model is specified as follows:
������ = �������� + �� + ��� + ��� + �� + ���� + ����; ��� = ��(���) + ���; = !(") + 24 + �,
(2)
where c(i) is the birth cohort of person i, �� is a birth cohort effect and �� is a calendar time shifter
allowing for the possibility of aggregate changes of the permanent earnings process over time. The
intercept and the slope of the individual-specific linear profile of earnings are factored into three
zero-mean components, with their variances capturing family (f), school (s) and neighborhood (n)
heterogeneity in initial earnings (denoted by ��, �� , ��) and life-cycle earnings growth (denoted
by �� , �� , ��).
The assumptions on the variance-covariance structure of permanent earnings are as follows:
(��&', ���)~�0,0; )*+,-& , ).-& �, / = 1,2; (3.a)
��� , ���~�0,0; )12& , )32& , )132�; (3.b)
(��, ��)~�0,0; )14& , )34& , )134�; (3.c)
(�� , ��)~�0,0; )15& , )35& , )135�, (3.d)
where the specific dimensions of heterogeneity of the variance-covariance parameters are denoted
by Φ (for family), Σ (for school) and Ν(for neighborhood).
Assumption (3a) allows the idiosyncratic parameters to vary by siblings’ birth order, which
we denote by b. We include singletons among the first born. Assumptions (3.b-3.d) specify the
distribution of the shared components and allow for unrestricted covariance (denoted by
)132, )134, )139) of initial heterogeneity and growth rate heterogeneity within each component.
11
We also model the sorting of families across communities by allowing for the covariance
between family and community effects, as well as for the covariance of school and neighborhood
effects between families that share the community:
!:��� , ��� = )24; !:���, ��� = )25; !:(�� , ��) = )49. (3.e)
Correlation across family and community effects is allowed through the intercepts of the
individual-specific profiles. This choice is made because empirically most of the community
effects vanish after two or three years (see Figure 4), and in order not to overcrowd the parameter
space.7 The first two covariances ()24 and )25) are non-zero if families sort themselves across
communities. The third parameter ()49) is a contextual term capturing the similarity of family
characteristics in the community, which induce a positive covariance between school and
neighborhood effects.
2.2 Specification of transitory earnings
We model transitory earnings (v) in equation (1) to capture any serial correlation of transitory
shocks using an AR(1) process. We allow siblings to draw shocks from birth-order-specific
distributions and we account for age effects in the variance of these shocks through an exponential
spline. Our model for transitory earnings can be summarized as follows:
����� = ;�<�����; <����� = =-<����(���) + >�����; (4)
>�����~�0, )?-& exp�C-(�)��, <����&'~�0, D�)E+,-& �,
where ;� is a time loading factor and <����� is the birth-order-specific AR(1) process with birth
order denoted by the index b. The autoregressive process begins at age 24 and we specify the
7 Allowing for sorting effects also in the slopes of the HIP model resulted in some negatively estimated variances for the slopes, indicating lack of identification for that parameterization in our data. We could estimate sorting effects of both intercepts and slopes without identification issues in simpler models that consider one dimension of community, either school or neighborhood. Including sorting effects in the slopes of the HIP model did not alter our substantive conclusions.
12
variance of the initial condition, denoted by )E+,-& , to be birth-cohort-specific with parameter D�.
The process evolves through the arrival of white noise shocks (denoted by >) whose variance is
age-and-birth-order-specific ()?-& exp�C-(�)�, with C-(�) denoting a linear spline in age with
knots at 28, 33, 38 and 43.
We allow transitory earnings to be correlated across individuals. The specific way in which
we model such correlation depends on the type of relationship between individuals. For siblings,
the use of birth-order-specific distributions of shocks enables identifying the contemporaneous
correlation of AR(1) innovations. Let " and "F index two individuals; the sibling covariance of
AR(1) innovations is specified as follows:
�>�����>�G��G�G�G� = )� , ∀ I, IF, J, JF, � = �F ± |!(") − !("F)|. (5)
That is, when the two individuals belong to the same family and when their age difference is such
that the two shocks belong to the same time period, then these shocks are allowed to covary with
parameter )� . This covariance of shocks between siblings does not depend on whether they
attended the same school, or lived in the same parish and is transmitted to later time periods
through the autoregressive structure of the model.
Due to the high dimensionality that would result from parameterizing the covariance of
shocks between numerous community members belonging to different families (O and OF), we
follow a different approach to that used for pairs of siblings. We allow for catch-all “mass-point”
covariances (P) collapsing all the parameters of the underlying stochastic processes, and allow
such covariances to fade away over time. For any two non-necessarily different age levels � and
�F, covariances of transitory shock across non-sibling peers are specified as follows:
13
�<����� <�G�G���G� = P���QR���GR, �<�����<�G�G��G�G� = P��QR���GR
�<�����<�G�G�G��G� = P��QR���GR, RPSR < 1, U = IJ, I, J.
(6)
2.3 Identification of permanent earnings components
In this sub-section, we discuss the identification of the permanent earnings components, which
besides time and cohort effects, includes three sets of parameters: i) family effects, ii) community
effects and iii) sorting effects. Assumptions (3.a) – (3.e) fully specify the intertemporal and
interpersonal distribution of permanent earnings. Identification of parameters is achieved by
exploiting three different types of moment restrictions (earnings covariances) generated by the
model: i) for siblings who share the community, ii) for siblings who do not share the community
and iii) for non-sibling peers.
For a given individual, earnings covariances between two time periods are a function of all
sources of earnings heterogeneity, which include the idiosyncratic component, as well as the
components due to the influences from the family, the school and the neighborhood. The moment
restrictions for a single individual for two non-necessarily different age levels � and �F can be
written as follows:
�������, ������G� = (7)
V)�Φ2 + )�Σ2 + )�Ν2 + �)�Φ2 + )�Σ2 + )�Ν2 ���′ +
�)132 + )134 + )139�(� + �F) + 2)24 + 2)25 + 2)45 +
)�24/2 + )�/2 X"J(�, �′)Y�!2� � ′ .
Cross-person moments (between siblings, neighbors, or schoolmates) do not depend on
idiosyncratic heterogeneity. Moment restrictions between siblings (different i but same f) depend
on the family effects and sorting effects. Moreover, they are also functions of school effects,
14
neighborhood effects, both, or neither, depending on the extent to which siblings share schools
and/or neighborhoods. Moment restrictions for siblings can be written as follows:
������� , ��G��G�G�G� = V)12& + )32& ��F + )132(� + �F) +
Z(I = IF)�)14& + )34& ��F + )134(� + �F)� +
Z(J = JF)�)19& + )39& ��F + )135(� + �F)� +
2)24 + 2)25 + 2)45[����G����G ,
(8)
where Z(. ) is an indicator function.
Equation (8) nests moments restrictions for four types of siblings who: (1) share both the
school and the neighborhood, i.e. Z(I = IF) = 1 and Z(J = JF) = 1; (2) share only the school, i.e.
Z(I = IF) = 1 and Z(J = JF) = 0 ; (3) share only the neighborhood, i.e. Z(I = IF) = 0 and
Z(J = JF) = 1; and (4) share only the family but neither the school nor the neighborhood, i.e.
Z(I = IF) = 0 and Z(J = JF) = 0.
The above moment conditions permit the identification of community effects separately
from family and sorting because not all sibling pairs share the community (school and
neighborhood). Since communities are defined on the basis of individual year of birth, siblings can
be exposed to different communities (school, neighborhood or both) because of family mobility in
the time window between the years each sibling turned 15, where age 15 is the year we use to
define communities. This variation in community exposure due to family mobility within a
specific time window – after the year the older sibling turned 15 and before the year the younger
sibling turned 15 – allows separating community effects from family effects. Within-family
variation in communities represents the key source of variation for our identification strategy.
15
To see this in equation (8), for siblings that share both components of the community, i.e.
Z(I = IF) = 1 and Z(J = JF) = 1 , the covariance function depends on family, sorting, and
community effects. For siblings that do not share the community, i.e. Z(I = IF) = 0 and Z(J =JF) = 0, the covariance function depends only on family and sorting effects. This is the case in
which siblings attended different schools at age 15 and lived in different neighborhoods because
the family moved in the time window between the years each sibling turned 15. The difference in
covariance functions between these two types of siblings identifies the sum of school and
neighborhood effects.
We can further disentangle school from neighborhood effects using siblings that share only
one component of the community effect, i.e. Z(I = IF) = 1 or Z(J = JF) = 1 . For them, the
covariance function depends on family and sorting, plus the common community component. This
is the case in which siblings attended different schools at age 15 but lived in the same
neighborhood, or lived in different neighborhoods at age 15 because of family mobility between
the years each sibling turned 15, but attended the same school. The difference in covariances
between families sharing both community dimensions and those sharing only one dimension
identifies heterogeneity in the non-shared dimension.
The within-family variation in community exposure that we exploit for identifying
community effects rests on the assumption that families changing community in this specific time
window are not selected and can be compared with families in which siblings reside in the same
community in the year they turn 15. However, these two types of families may be different due to
underlying unobserved characteristics that also affect earnings. To support the validity of the
identifying assumption, we also exploit differences in the timing of family mobility and perform
the analysis focusing only on families who moved.
16
Siblings who share the community in the year they turn 15 belong to two different types of
families: i) families who never moved, and ii) families who moved before the older sibling turned
15. Therefore, instead of comparing moving to staying families, we can compare families who
moved after the older sibling turned 15 with families who moved before the older sibling turned
15. These are all families who move, so it is only the difference in the timing of mobility that
exposes siblings to different environments. This is plausibly exogenous variation which can be
argued to be less prone to selection than contrasting movers and stayers. We show in Section 5.3
that our results are robust when variation is restricted only to movers exploiting differences in the
timing of family mobility.
Although moment conditions for siblings can identify community effects, they are not
sufficient to separate family effects from sorting. This is evident from the fact that the term
2)24 + 2)25 + 2)45 enters equation (8) irrespective of whether siblings went to the same school
or lived in the same parish. Because families sort across schools and neighborhoods, school and
neighborhood effects are always correlated between siblings, and such covariance is not separable
from the variance of family effects in equation (8). To separately identify the sorting parameters
)24, )25 and )45 from the family effects, we exploit moment restrictions for non-sibling peers
(neighbors and schoolmates) that by definition do not share the family (O ≠ O′): ������� , ��G�G�G�G�G� =
VZ�I = I′��)�Σ2 + )�Σ2 ��′ + )��Σ�� + �′� + 2)ΦΣ� +
Z(J = JF)�)19& + )39& ��F + )135(� + �F) + 2)25� + 2)45[��&����G . (9)
For non-sibling peers, the covariance function depends on community and sorting effects.
Because community effects are already identified by the moment restrictions for siblings, moment
restrictions in (9) effectively identify sorting of families across communities. Equation (9) nests
17
three moment restrictions (for peers sharing both school and neighborhood and for peers sharing
either school or neighborhood) which provide identification for the three parameters )24, )25 and
)45. Identification is achieved thanks to the partial overlapping of peer groups, which depends on
the design of school catchment areas across parishes (see Section 3).
Finally, combining the moment restriction of equation (8) – which provides both the total
sibling effect and the identification of community effects – with those of equation (9) – which
provides identification of sorting effects – we identify family effects.
The key difference between our research design and that of the sibling correlation literature
is that by defining communities on the basis of individual year of birth we can separately identify
sorting from neighborhood, school and family effects by exploiting arguably exogenous family
mobility across communities based on differences in the timing of mobility and the partial overlap
of schools and neighborhoods. Earlier research could not separate community from sorting effects
because – due to the sampling design – siblings always shared the community. We are the first to
estimate both the sorting and contextual covariances within sibling covariances.8
2.4 Estimation and decomposition of the sibling correlation
The model is estimated by Minimum Distance matching moment restrictions implied by the model
to the empirical moments derived from the data.9 As mentioned earlier, the empirical moments are
based on the residuals, after regressing log real gross annual earnings on year dummies and a
quadratic age trend by birth cohort. There are three types of empirical moments entering into the
estimation. First, there are individual moments, which include the variances and intertemporal
8 Raaum, Sørensen and Salvanes (2006) use a linear projection of earnings on neighborhood characteristics and neighborhood fixed effects to derive an approximation for the contextual term. 9 Moment restrictions for transitory earnings are given in the Appendix. The orthogonality assumption between permanent and transitory earnings in equation (1) implies that moment restrictions of the full model are the sum of moment restrictions for permanent and transitory earnings. We use Equally-Weighted Minimum Distance (see, for example, Haider, 2001).
18
covariances of individual earnings. Second, there are sibling moments, which are defined only in
families where there are at least two brothers. This implies that each family contributes at most
once in the estimation of sibling empirical moments, but families with only one son do not
contribute. We estimate separate empirical moments for siblings depending on whether they
shared the school, the neighborhood, both or neither, so as to match the four different moment
restrictions that are nested in equation (8). Finally, there are empirical moments for non-sibling
peers who shared the community. In contrast to families, the number of peers varies within
community clusters. We account for such varying importance of community clusters using the
weighting scheme proposed by Page and Solon (2003, pp. 841). In particular, we first estimate the
within-cluster covariances and then we take the between-cluster weighted average of within-
cluster covariances using weights that are proportional to the number of individuals in that cluster.
Similar to the case for siblings, we estimate empirical moments distinguishing whether peers
shared the school, the neighborhood, or both.
Using parameter estimates from the model we can predict the contributions of family and
community to the sibling correlation of permanent earnings over the life cycle. For this purpose,
we can use moment conditions (8) and (9) and attribute sorting parameters, whose allocation to
either factor is inherently ambiguous, in equal parts to family and to communities:
]^(�) = ������� , ��G��G�G�� − ����G����G()24 + )25) ������� , ������� ∀ I ≠ IF�J_ J ≠ J′,
]`(�) = �������, ��G�G��G�� − ��&����G()24 + )45) �������, ������� ∀ O ≠ OF�J_ J ≠ J′, (10)
]a(�) = �������, ��G�G�G��� − ��&����G()25 + )45) ������� , ������� ∀ O ≠ OF�J_ I ≠ IF,
19
where r denotes correlation coefficients of permanent earnings, while F, S and N denote the three
relevant dimensions of heterogeneity (family, school, neighborhood). It should be emphasized that
correlations vary with age because they are estimated from a model of life-cycle earnings. Given
the model assumptions, the sibling correlation of permanent earnings (]b(�)) for brothers sharing
the community is the sum of the three components:
]b(�) = ]^(�) + ]`(�) + ]a(�) (11)
3. Data
3.1 Sample Selection
We use data from administrative registers of the Danish population. The civil registration system
was established in 1968 and everyone resident in Denmark then and since has been registered with
a unique personal identification number, which has subsequently been used in all national registers
enabling accurate linkage. In our analysis we consider only males and we construct our dataset as
follows. First we create a sample of brothers by sampling fathers and finding their first and second
born sons. Second we link sons to their teenage communities of neighbors and schoolmates. In
order to create our dataset of brothers we consider men born in the years 1960-1983 and select first
and second sons who share both legal parents from registration at birth and are not adopted. The
year of birth selection starts in 1960 because of prior incompleteness of registered parentage and
stops in 1983 to allow observation of individual earnings up to the late 20s for younger cohorts
(earnings data described later in the Section are available until 2011).10 We exclude from the
sample sons who are also observed as fathers, brothers born less than 12 months apart and brothers
who are born more than 12 years apart. In this way we obtain 122,652 sibling pairs. Following the
10 Subsequent sons beyond the first two are very few (4 percent) and are not considered in the analysis. The son birth order is determined irrespective of daughters present in the family.
20
tradition in the sibling literature we keep singletons (men without a younger brother) in the
sample; there are 380,948 singletons in the sample. The robustness analysis in Section 5 shows
that excluding singletons does not affect our findings.
Next we link our sampled brothers (and singletons) to all other males who are born in the
same year and share their youth communities (schools or neighborhoods). In contrast to our
treatment of siblings, peers are included in the analysis irrespective of birth order and age spacing
from their own brothers, which adds 69,708 individuals to the analysis. Using information from
the educational register, we link pupils to schoolmates on 31 October of the calendar year they
turn 15, which is in the academic year they would normally attend 9th grade.11 Our sample
contains 1,858 schools with males aged 15. They have on average 19.5 male schoolmates born in
the same calendar year. Using information on individual addresses obtained from the central
person register, we define neighborhoods as the parish of residence. Individuals are required to
report changes of address to the municipality within five days. As with schools, our census point is
31 October of the calendar year a male turns 15. There are 2,123 parishes in our sample containing
on average 14.6 males turning 15 in the same year.12
School enrolment rules were such that pupils should start in first grade in the August of the
calendar year they turn 7. The national pupil database was established to monitor compliance with
the 1972 school reform, which made 8th and 9th grade schooling compulsory in 1972/3 and
1973/4 respectively. Beginning in August 1973, the database links pupils to the schools they are
11 In 1980, 95 percent of pupils began 9th grade during the year they turned 15. In recent years delays have been more common – in 2007, 13 percent of pupils delayed their school start by a year and 4 percent repeated the same grade the following year. 12 Complete information on municipality of residence is available from 1971 and full addresses are complete from 1977 (see Pedersen, et al. 2006 for details). We use an intermediate aggregation of locality as our neighborhood indicator – parish of residence – which is available from 1973.
21
enrolled from 8th grade and above.13 School identifiers are consistent over time and schools are
classified according to whether they are publicly run (77% of schools and 89% of pupils in our
estimation sample) or privately run, and whether they are exclusively for pupils with special
educational needs (10% of schools and 1% of pupils in our gross sample).14
During our sample period, pupils were assigned to public schools on a catchment area basis
according to place of residence. Primary and lower secondary education usually takes place in the
same school and most pupils attend the same school for all grades. From 2007 we can see that
92% of pupils in grades 1-8 were enrolled in the same school the following year. Due to the
organization of primary and secondary schools largely as a single unit, there is likely to be less
pupil mobility between schools than in other countries. This institutional setting makes Denmark a
good place to look for school effects, because of the coherence of the schoolmate group.
Also, an important Danish institutional feature is that parishes and public school catchment
areas do not completely overlap. As a consequence, neighbors may attend different schools, and
schoolmates may come from different neighborhoods. Amongst school-birth-cohort clusters, 89.5
percent have individuals from more than one parish, and amongst parish-birth-cohort clusters 60.1
percent have individuals from more than one school.
Because communities are defined on the basis of individual year of birth, not all brothers
will share the community. Among our 122,652 brother pairs, 70 percent share both schools and
neighborhoods at age 15, 5 percent share only the school, 16 percent share only the neighborhood,
while the remaining 9 percent do not share either component of the youth community.
13 In anticipation of grade K enrolment being made compulsory from August 2009, the national pupil database was extended to cover grades K-7 from August 2007. Hence, we are unable to match pupils to schoolmates in earlier grades to look at long run outcomes. 14 We exclude from our estimation sample individuals enrolled at schools which are exclusively for pupils with special educational needs. Private schools are smaller on average than public schools, are primarily in urban areas and are heavily subsidized, with municipalities covering 85 percent of expenditure. In sensitivity analysis we show that results are robust to private school exclusion.
22
For both brothers and for peers we use pre-tax annual labor earnings between 1984 and
2011, measured in 2005 prices. We select all valid observations on earnings and exclude zero-
earnings observations. The exclusion of zero-earnings observations is common with most of the
earnings dynamics literature assuming that earnings are missing at random, and is also applied in
the sibling correlation literature by Björklund et al (2009). We ‘trim’ a quarter of a percentile from
each tail of the annual earnings distribution and require at least three consecutive earnings
observations for an individual to be included in the sample, a selection rule that is intermediate
between the one used by Baker and Solon (2003), i.e. continuous earnings strings for each
individual within a cohort, and the approach of Haider (2001), who allows individuals to move in
and out of the sample only requiring two positive but not necessarily consecutive valid
observations on earnings.
Table 1 presents the cohorts we include in the sample, the years for which we observe
earnings and sample sizes in various dimensions. Following Baker and Solon (2003), we group
data in two-year birth cohorts, as shown in column 1, and we compute age by imputing each
cohort with its first year of birth. The selection of birth cohorts and time window ensures that each
cohort is observed starting at age 24 for at least 6 years (last cohort 1982) and for as long as 28
years (first cohort 1960). Columns 5 and 6 present the number of earnings observations and
number of men used in estimation. The number of community cohorts into which men are grouped
is shown in columns 7 and 8, totaling 33,907 school cohorts and 47,622 parish cohorts.
Half of earnings observations are from the first third of birth cohorts. Cohort size peaks in
1966-7 and falls by 44 percent by the last cohorts in 1982-3. Number of school cohorts and parish
cohorts is quite stable, reflecting an absence of administrative unit reform. Population
demographics dictate birth cohort sizes and the falling number of earnings observations by birth
cohort is due to later cohorts having less time to accumulate earnings histories.
23
3.2 Sample comparison to other studies
It is informative to contrast our neighborhood definition with that used in comparable studies such
as Page and Solon (2003), Raaum, Sørensen and Salvanes (2006) and Oreopoulos (2003).15 Table
2 characterizes ours alongside these three other studies according to characteristics of the different
types of neighborhoods and exposures considered, and outcomes observed. Neighborhood
geography and exposure group – an area and an age range – together define the cluster of
individuals within which later outcomes are correlated. Neighbors in study (3) have the closest
proximity because of the medium-to-high density of housing projects, followed by study (1)
because of the clustered PSID sampling frame. Interestingly, study (1) finds neighborhood effects
only for urban areas, where neighbors are in closest proximity. Our Danish parishes cover a wider
area than the neighborhoods used in studies (1) and (3), but are only about half the size of
Norwegian census tracts used in study (2). For Denmark in the year 2000 we can calculate the
distribution of distances between the different residences of 15 year olds within parish: 25 percent
of distances are within 0.5 km, 50 percent within 1.1km, and 75 percent within 1.9km.
The other three studies pool neighbors together of different ages – with up to 9 and 11
years age differences – to form neighborhood clusters. In the main part of the analysis we consider
neighbors at 15 years of age as belonging to the same cluster. Neighborhood exposure at age 15 is
at the upper end of the 5-16 age range together considered in the other studies. All else equal, if
neighbors of the same age are more likely to interact than neighbors of different ages, then we
would expect to find stronger neighbor correlations with our definition. In sensitivity checks we
show robustness of results to neighborhood definitions based on exposure down to age 10.
15 In what follows we refer to Page and Solon (2003) as study (1), Raaum, Sørensen and Salvanes (2006) as study (2) and Oreopoulos (2003) as study (3).
24
The number of men in each of our neighborhood clusters is in the middle of the range for
the other studies. The estimation sample in studies (1) - (3) comprises a similar percentage of the
total population of individuals in each cluster with 4.6, 3.1, and 4.8 percent respectively. Due to
our narrower age range for clustering neighbors for Denmark the estimation sample covers only
0.6 percent of the cluster population. Although our neighbors are more homogeneous in terms of
age, they represent only between one eighth and one fifth of the within-cluster sampling density of
the other studies. However, this sparser sampling would reduce precision rather than introduce any
bias.
The duration of neighborhood exposure observed for an individual differs between studies,
with only study (3) using more than a single point in time. Although studies (1) and (2) consider a
range of ages of exposure, attachment to a neighborhood is only considered at a single point in
time, just as in our study. The persistence of neighborhood affiliation is likely to differ between
contexts, and this will affect saliency of the neighbor groupings used, but it is difficult to establish
how important this might be for explaining differences in findings between studies. In sensitivity
analyses, we use alternative definitions for neighbors based on those living in the same parish at
each age 14 to 15, at each age 10 to 12, or based on the more frequent parish of residence between
ages 14 to 18.
4. Descriptive statistics on earnings of siblings and non-sibling peers
In this section we provide a description of the interpersonal covariance structure of earnings. There
are two types of cross-person relationships that are of interest to our analysis: 1) between siblings
(brothers) and 2) between male non-sibling peers attending the same school and/or residing in the
same neighborhood (parish) at age 15.
25
For brothers, we compute the covariance of their earnings from families with at least two
male children. For male non-sibling peers, we group them in clusters depending on whether they
share the school and the neighborhood, only the school, or only the neighborhood. We obtain the
between-peers covariance of earnings (at each relevant age) by first computing the within-cluster
covariance and then averaging covariances between clusters using the weighting scheme of Page
and Solon (2003, pp. 841), which gives more importance to more populated clusters, and makes
inference person-representative.
We begin by describing the correlation of sibling earnings by age in Figure 1. The solid
line labeled “At same age” reports the computed correlation when the brothers are at the same
point in their life cycle, a comparison that is available in our data. The earnings correlation
declines between age 24 and 30 and remains stable after age 30. The decline suggests that sources
of initial earnings heterogeneity shared between brothers are negatively correlated with
heterogeneity in earnings growth. As discussed in Section 2.1, human capital models predict
investments in education or training to induce such a negative correlation. The dotted line fixes the
age of the older among the two brothers at age 35 and reports the sibling correlation by age of the
younger brother. In this case, the earnings correlation is relatively low at age 24 (actually close to
zero) and increases sharply so that by the early-30s it matches the “same age” correlation. This
pattern illustrates that the earnings correlation between siblings of different ages is an
underestimate of the correlation one would obtain observing siblings at the same point in their life
cycle. This is a form of life-cycle bias as discussed in Haider and Solon (2006). The figure shows
that we can observe this bias in the data, which suggests that we have the information required for
controlling it in estimation.
Besides human capital investments, the large contemporaneous associations at the early
stage of the life cycle depicted in Figure 1 may also reflect the correlation of transitory shocks. It
26
is well known that earnings instability is large in the beginning of the working life (see e.g. Baker
and Solon, 2003). It is also plausible that siblings may be subject to common shocks; for example
due to similar local economic conditions at labor market entry. As a way to assess if the relatively
large sibling correlation at labor market entry is driven by permanent earnings differences or
transitory fluctuations, in Figure 2 we present the earnings correlation for brothers born at least
five, eight or ten years apart. The larger the age difference, the less likely it is for brothers to enter
the labor market at the same time and share transitory shocks. Therefore, these samples are less
likely to be influenced by transitory fluctuations compared with the samples underlying Figure 1.
As Figure 2 shows, the declining pattern of the sibling correlation between the mid-20s and the
early-30s persists even after excluding closely-spaced-brothers who are more likely to share
transitory earnings fluctuations. This suggests that the source of the convex evolution of sibling
correlations shown in Figures 1 and 2 is in the permanent earnings component.
In Figure 3, we plot the earnings correlations for male non-sibling peers at the same point
in their life cycle distinguishing between those sharing both the school and the neighborhood,
sharing only the school, or only the neighborhood. These empirical correlations pick-up all sources
of peer similarity, which include both those correlated with family effects and those independent
of them. There are a few points worth highlighting in this figure. The first is related to the
magnitude of the earnings correlation of non-sibling peers, which is roughly one tenth of the
correlation of sibling earnings reported in Figures 1 and 2. Second, the earnings correlation is
higher at the beginning of the life cycle and up to age 30, which implies that after that age the
influence of peers appears to be negligible. Third, schools seem to exhibit stronger influence
compared to neighborhoods. Finally, Figure 3 also reports the correlation of earnings for
“Unrelated” individuals, who do not belong to the same family and who are neither schoolmates
nor neighbors in the parish of residence. We compute this correlation by randomly matching each
27
individual in the sample with 1000 unrelated individuals of the same age. We find this correlation
to be equal to zero for all ages, which suggests that the evolution of sibling and non-sibling peer
correlations over the life cycle is picking up some underlying forces due to families, schools and
neighborhoods, and is not simply an artifact of age effects.
5. Results
We concentrate the discussion on estimates for the ‘core’ parameters of the permanent and
transitory components, which we present in Section 5.1. 16 In Section 5.2, we discuss the
decomposition of the sibling correlation and compare the main findings with the existing evidence
in the literature. In Section 5.3, we provide evidence for the validity of our identification strategy
comparing the results of the full sample to those exploiting differences in the timing of family
mobility among moving families. Finally, in Section 5.4 we present a set of sensitivity checks
related to the sample and the measurement of community membership.
5.1 Parameter estimates
5.1.1 Permanent earnings
Based on equation (2), permanent earnings depend on shared and idiosyncratic components. The
parameter estimates for the shared components reported in Panel A of Table 3 show that family is
by far the most relevant factor for long-term earnings. This is true both for initial earnings
16 Parameter estimates of the time and cohort effects on both components are reported in Tables A1 and A2 of the Appendix. Their identification requires setting one parameter for each component and each dimension (time and cohort) equal to one. Exceptions are the cohort shifters on the initial condition of the transitory component (D�). Because the model includes not only the variance of shocks at age 24 ()E+,-& , the initial condition) but also a specific
parameter for the variance of innovations at age 25 ()?-& ), representing the baseline of the age spline, there is an additional cohort shifter that needs to be constrained. Empirically, we find estimates of shifters on the two oldest cohorts to be imprecise and negative, and we constraint also those two shifters.
28
(intercept) and for earnings growth rates (slope). The other relevant source of permanent inequality
in earnings is the individual idiosyncratic component reported in Panel B of Table 3.
Shared components of long-term earnings in Table 3 display the Mincerian cross-over
property. This is indicated by the negative covariance between intercepts and slopes of earnings
profiles ()132, )134, )139 ), which suggests that families or communities associated with low
earnings at age 24 are also associated with faster growth in life-cycle earnings.17 A corollary of the
negative covariance is that the variance of permanent earnings across families or communities is
U-shaped in age because it falls in the years of catch-up and increases after the point of cross-over.
The point of cross-over can be computed as the year in which the earnings variance is minimized,
and it is located at age 31 for the between-family earnings distribution, at age 34 for the between-
neighbors earnings distribution, and at age 39 for the between-schoolmates earnings distribution.
The covariances between the three components of shared earnings determinants ()24, )25
and )45) capture sorting of families into schools and neighborhoods. The estimates in Panel A
suggest that sorting is relevant, as the covariances of family effects with school and neighborhood
effects ()24, )25) are positive, sizeable and statistically significant. These effects imply that a
high draw from the distribution of family effects in permanent earnings is associated with similarly
high draws in the distributions of school and neighborhood effects. We also find a positive
covariance among community effects ()45), which suggests that school and neighborhood effects
are positively correlated because similar families choose similar schools and neighborhoods.
5.1.2 Transitory earnings
Parameter estimates of transitory earnings in Table 4 show a clear age pattern of transitory shocks
whose variance decreases between the mid-20s and the mid-30s, while the decrease slows down 17 Taking into account that sorting contributes to the variance of intercepts, the correlation between intercept and slope is equal to -0.725.
29
around age 35. This sharp decline followed by a leveling-off is consistent with the patterns
reported by Baker and Solon (2003) who find that the variance of transitory shocks declines at
decreasing rate between the ages of 25 and 45. The patterns that we find by age are very similar
between brothers. Autoregressive coefficients are also very similar between brothers, and are of
moderate size. Finally, Table 4 shows that the correlation of transitory shocks between siblings or
non-sibling peers is generally not statistically significant, with the exception of the correlation
among schoolmates.18
5.2 Decomposition of sibling correlation
We can assess the relative importance of family, community and sorting by considering the
decomposition of the sibling correlation at age 24. This is because the model allows for sorting of
families across communities only within the intercept of the model, and the initial point of the
income profile is set at age 24. Using the average of brothers’ random walk intercepts as a measure
of initial idiosyncratic variance, the overall sibling correlation is equal to 0.75.19 The part of the
sibling correlation that is accounted for by family effects is equal to 0.48, while the part accounted
for by community effects and sorting is equal to 0.12 and 0.15, respectively. This suggests that
communities alone exert only a small effect on earnings inequality measured at age 24.
We now move to the decomposition of the sibling correlation throughout the life cycle. We
use the estimates reported in Table 3 to generate predictions of the sibling correlation and its
decomposition into the three factors of interest (family, school and neighborhood) based on the
formulae provided in Section 2.4 (equations 10 and 11), imputing estimated sorting parameters to
family and community in equal parts. In particular, we consider the case represented by equation
18 Background analysis shows that these parameters are still small but statistically significant if we exclude cohort effects from the model.
19 This is computed using the following formula: ]&'b = cde+ Qcdf+ Qcdg+ Q&cefQ&cegQ&cfgh.i�cj+,,k+ Qcj+,,++ �Qcde+ Qcdf+ Qcdg+ Q&cefQ&cegQ&cfg.
30
(11) of two brothers who attend the same school and live in the same neighborhood at age 15. The
resulting sibling correlation is the sum of family, school and neighborhood effects.
As shown in Figure 4, the life-cycle pattern of the sibling correlation is U-shaped in age.
More specifically, the estimated sibling correlation is equal to 0.57 (s.e. 0.11) at age 25, drops to
0.19 (s.e. 0.121) at age 35, and rises back to 0.43 (s.e. 0.014) by age 49, which is the last age for
which we observe younger brothers. The average sibling correlation over the life cycle, reported in
Column (1) of Table 5, is equal to 0.32 (s.e. 0.010), which is in line with previous estimates for
Denmark.20 As mentioned earlier, the U-shaped pattern is a symptom of the “Mincerian cross-
overs” of earnings profiles. That is, the negative estimates of the covariance between the intercept
and the slope of the earnings profiles implies that the distribution of shared components, and
therefore the siblings and non-sibling peers correlation, first shrinks and then fans out over the life
cycle. The same U-shaped pattern is also a feature of the raw cross-person correlations shown in
Figures 1 to 3, and especially in Figure 2, which depicts the earnings correlation for brothers born
only a few years apart.
Considering the decomposition of the sibling correlation, it is evident from Figure 4 that
family is far more important than community in influencing the dispersion of permanent earnings
over the life cycle. The community effects are limited and are only significant at the beginning of
the working life, while by age 30 they become negligible and not significantly different from zero.
In particular, the estimated community correlation of earnings (the sum of neighborhood and
school effects) is equal to 0.21 (s.e. 0.021) at age 24, drops to 0.053 (s.e. 0.010) at age 27 and
becomes zero at age 30. As reported in Column (1) of Table 5, on average over the life cycle the
estimated correlation in permanent earnings is equal to 0.011 (s.e. 0.010) across schoolmates, and
20 Using a model without community effects, Björklund et al. (2002, p. 765) report for men aged 25-42 a sibling correlation of 0.29. We obtain an average estimate of 0.28 if we limit our sample in the same age range.
31
0.010 (s.e. 0.010) across neighbors. In both cases, the estimates are close to zero and not
statistically significant. The overall correlation for community effects is small (0.021) and
marginally significant (s.e. 0.009). These results indicate that there is not much room for
community effects in shaping the sibling correlation in the long run. The family is the only factor
that generates a substantial correlation in permanent earnings between brothers throughout the life
cycle.
One implication of the decomposition depicted in Figure 4 is that measuring earnings at
relatively young ages exaggerates the long run relevance of community effects. For example, the
share of sibling correlation accounted for by community effects is 27, 24 and 19 percent, if
earnings are measured up to ages 25, 27 and 30, respectively. However, the corresponding figure
is only 6 percent if we consider the entire available life-cycle profile up to age 49. This shows the
importance of analyzing earnings beyond the early part of the working life.
Our findings compare with those of Oreopoulos (2003) who finds a zero correlation of
earnings between neighbors after accounting for sorting of families into neighborhoods by using
quasi-random assignment of neighbors. Without taking sorting into account, Page and Solon
(2003) find a positive correlation of neighbors earnings in the PSID equal to 0.16, which is half of
their estimated sibling correlation of 0.32. Raaum, Sørensen and Salvanes (2006) report a youth
neighbors’ earnings correlation of 0.06 and a sibling correlation of 0.2, implying an incidence of
30 percent of neighborhood effect over the total sibling correlation.
The key feature of our sample design is that we exploit variation of communities within
families, which combined with the partial overlap of schools and neighborhoods, enables
disentangling family, community and sorting effects. In addition, within our model we can
compare our baseline results with the case in which we ignore sorting in the following two ways.
First, we can restrict the sample of siblings only to those who share both the school and the
32
neighborhood. In this case only two out of three sets of parameters (family, community, sorting)
are identified, so we restrict the sorting effects to zero. Second, we can exclude sibling moments
altogether and constrain the family-related model parameters to be zero. In both cases, by ignoring
the sorting of families into communities, the community effects should capture not only the effects
of communities but also pick up the influence of families.
We present the results from these restricted models in Columns (2) and (3) of Table 5.
Column (2) shows that the incidence of the community effect over the overall sibling correlation
grows from 6 percent in the baseline (=0.02/0.32) to 14 percent (=0.045/0.31) in the sample where
siblings always share the community. In Column (3), we present the results when we estimate the
model excluding family information altogether. The correlation between non-sibling peers, that
includes community and sorting effects, increases to 0.07, or 21 percent of the baseline sibling
correlation. These restricted models suggest that, when family is ignored, the community effects
are upward biased by a factor of three and are closer to the estimates reported in studies which do
not account for sorting.
5.3 Robustness of identification
In this sub-section, we check the validity of our identification strategy by exploiting differences in
the timing of family mobility and focusing only on siblings whose families have moved across
parishes. Restricting the analysis only to movers can be argued to be less prone to selection.
Specifically, we use additional information on the residential location of parents when the siblings
were younger than age 15, which is available only for younger cohorts. In particular, the more
recent the cohorts we consider, the younger we can first observe parental residence. We focus on
33
cohorts born after 1965 for whom we know the parental parish back to age 10. We use mother’s
parish and we fill in missing information with father’s parish.21
Using the information on parental parish at age 10, within the selected birth cohorts, we
can partition siblings into three groups. The first group consists of siblings who reside in different
parishes at age 15. We label them as “late movers” because family mobility occurs after the 15th
birthday of the older brother and before the 15th birthday of the younger brother. The second group
consists of siblings who reside in the same parish at age 15 but for whom the parental parish of the
older brother changed between ages 10 and 15. We label this group of siblings as “early movers”
because family mobility occurs before the 15th birthday of the older brother. This second group of
“early movers” differs from the group of “late movers” because of the timing of family mobility.
Finally, there is the group in which parental parish of the older brother did not change from age 10
to 15. These are families that never moved, or moved before the older brother turned 10 and we
label them as “stayers”. Arguably, there is more similarity between “early movers” and “late
movers” than there is between “late movers” and “stayers”. To check the robustness of the
identification to selectivity between movers and stayers we repeat the analysis by restricting the
sample only to “early” and “late” movers.
We present the results of this robustness analysis in Columns (4) and (5) of Table 5. Column
(4) replicates the baseline model but limits the sample to the cohorts born after 1965 to provide the
correct benchmark for the robustness check. Column (5) reports results based on the same cohorts
as in Column (4) but restricting the sample only to movers.
We find that more recent cohorts are characterized by larger community effects compared to
the baseline, but they are still limited below 10 percent of the overall sibling correlation. When we
exploit only the contrast between “early movers” and “late movers” we find that the part of sibling
21 Parental parishes when the individual is age 15 coincide with individual parish at the same age for 95% of the cases.
34
correlation accounted for by community effects is equal to 14 percent (0.045/0.32), which is still
much lower than previous studies of sibling correlations. This evidence suggests that including
“stayer” families in the baseline sample lowers the estimated community effect. However, it does
not alter our main result that family accounts for most the sibling correlation and that community
effects do not persist in the long run. This conclusion is supported by looking at Figure 5, which
reports the life-cycle decomposition of the sibling correlation for cohorts born after 1965, both for
the full sample and for the sample of movers. The two graphs are very similar and, in particular,
the long-term level of the community effect is essentially zero, no matter which sample one
considers.
5.4 Sensitivity analysis
We subject our results to several sensitivity checks. We first estimate the model for different
family sizes (up to 2 or up to 3 children) and we exclude singletons. We report in Table 6 the
average over the life cycle sibling correlation and its decomposition for each of these sensitivity
checks. Overall, these different sample selections do not alter the main conclusion from the
baseline model.
We also check the sensitivity of our findings by varying the degree of exposure and the
definition of youth communities. One potential concern with the baseline model may be related to
the definition of community, which is based on membership only in one single year. By defining
communities only at age 15 we might miss part of the community effects due to potentially limited
exposure (see also Gibbons, Silva, Weinhardt, 2013, and Chetty, Hendren and Katz, 2016, for
similar discussions). To address this we re-estimate the model using two alternative criteria for
community membership, which are characterized by greater exposure to communities relative to
the one-year definition used in the baseline model. First, we define schoolmates and neighbors as
35
those sharing schools and neighborhoods, respectively, during both ages 14 and 15. Second, we
define the neighborhood as the prevalent parish of residence between ages 14 and 18.22
As we report in Table 6, none of these alternative definitions alters our finding that
community effects account for only a limited share of the sibling correlation in earnings. Defining
non-sibling peers as those sharing schools and neighborhoods both at age 14 and 15 yields an
average correlation of permanent earnings between schoolmates equal to 0.009 (s.e. 0.009), and an
average over the life cycle correlation between neighbors equal to 0.011 (s.e. 0.010). Similarly,
defining youth neighborhoods as the parish in which individuals lived most frequently between the
ages of 14 and 18, we find an average correlation of permanent earnings between neighbors equal
to 0.006 (s.e. 0.010), and an average correlation between schoolmates equal to 0.013 (s.e. 0.009).
We also report in Table 6 further robustness checks excluding private schools, or using the ZIP
code of residence at age 15 to define neighborhoods instead of parishes. In all cases we find our
baseline results to be very robust.
Another concern with the community definition might be that age 15 lies at the upper
bound of the age ranges that have been used by other papers in the literature. To address this
concern, we use the sample of cohorts born after 1965 for which we can observe parental parish
back to the year in which the individual was age 10. We report these results in Table 7. Moving
progressively back in time, the age in which we define parish affiliation does not affect the main
conclusion that the share of sibling correlation accounted for by community effects is generally
limited below 10 percent. Alternatively, we can use these cohorts in a model where community is
defined as the neighborhood of residence at ages 10 to 12 (excluding cases changing residence in
that age range) to see if there is any additional impact of prolonged early exposure. Even with this
22 More than three quarters of individuals in our sample (76.5%) do not change parish of residence between ages 14 and 18. We cannot apply a similar definition to schools because of compulsory schooling ending typically at age 15.
36
definition we find a limited role of community, which accounts for 8% of the overall sibling
correlation.
6. Conclusion
Exploiting population-based administrative data for Denmark, by virtue of which we can link
earnings records of siblings, schoolmates and parish neighbors, we analyze the relative influence
of family, schools and youth neighborhoods on earnings inequality. We develop and estimate a
model of the joint earnings dynamics of multiple groups of individuals, which accounts for sorting
and allows us to decompose for the first time the sibling correlation of earnings into family,
neighborhood and school effects over the life cycle. To separate the influence of family and
community attributes from sorting we exploit two sources of plausibly exogenous variation: i)
variation in community exposure, which arises because of family mobility, and more specifically,
due to differences in the timing of family mobility across siblings, and ii) variation due to the
partial overlap of schools and neighborhoods, which implies that neighbors may be enrolled in
different schools and schoolmates may come from different parishes.
This research design shows that, within the environment individuals grow up and live,
family is the most important factor in accounting for the inequality of permanent earnings over the
life cycle. Neighborhoods and schools influence earnings only early in the working life in an
almost equal way, but this influence falls rapidly and becomes negligible after age 30. This implies
that, when earnings can only be observed while relatively young, the influence of community on
long run earnings inequality is overstated.
Our findings are based on data from Denmark, which, because of its welfare system, is
typically considered to promote equality of opportunity. However, as highlighted recently by
Landersø and Heckman (2016), there is much less educational mobility than income mobility in
37
Denmark. Low private financial returns to schooling fail to incentivize educational investments
among the children of less educated parents. This is consistent with our finding that family is the
most important determinant of long run earnings similarities across siblings. Communities seem to
affect earnings early in the working life, for example through peers influencing educational
choices or youth behaviors, but these influences determine only short term deviations from an
earnings profile that – apart from idiosyncratic abilities – mainly reflects characteristics and
choices of the family. As administrative datasets and cohort studies mature in other countries, our
approach could be applied to measure family and community effects on long run outcomes in
other contexts.
38
References
Baker, Michael, and Gary Solon. 2003. “Earnings Dynamics and Inequality among Canadian Men,
1976-1992: Evidence from Longitudinal Income Tax Records.” Journal of Labor
Economics, 21 (2): 267-88.
Becker, Gary S., and Nigel Tomes. 1979. “An Equilibrium Theory of the Distribution of Income
and Intergenerational Mobility.” Journal of Political Economy, 87 (6): 1153-89.
Ben-Porath, Yoram. 1967. “The Production of Human Capital and the Life Cycle of Earnings.”
Journal of Political Economy, 75 (4): 352-65.
Bingley, Paul, and Lorenzo Cappellari. 2013. “Correlations of Brothers’ Earnings and
Intergenerational Transmission.” Dipartimento di Economia e Finanza, Università Cattolica
Working Paper No. 6.
Björklund, Anders, and Markus Jännti. 2009. “Intergenerational Income Mobility and the Role of
Family Background.” in Oxford Handbook of Economic Inequality, edited by Wiemer
Salverda, Brian Nolan, and Timothy Smeeding, 491-521. Oxford: Oxford University Press.
Björklund, Anders, Tor Eriksson, Markus Jännti, Oddbjrön Raaum and Eva Österbacka. 2002.
“Brother Correlations in Earnings in Denmark, Finland, Norway and Sweden Compared to
the United States.” Journal of Population Economics, 15:757–72.
Black, Sandra E., Paul J. Devereux. 2011. “Recent Developments in Intergenerational Mobility.”
in Handbook of Labor Economics, Vol. 4A, edited by Orley Ashenfelter and David Card,
1487-541. Amsterdam: Elsevier Science, North Holland.
Black, Sandra E., Paul J. Devereux, and Kjell G. Salvanes. 2005. “The More the Merrier? The
Effect of Family Size and Birth Order on Children's Education.” The Quarterly Journal of
Economics, 120 (2): 669-700.
39
Black, Sandra E., Paul J. Devereux, and Kjell G. Salvanes. 2013. “Under Pressure? The Effect of
Peers on Outcomes of Young Adults.” Journal of Labor Economics, 31 (1): 119-153.
Blundell, Richard, Luigi Pistaferri, and Ian Preston. 2008. “Consumption Inequality and Partial
Insurance.” American Economic Review, 98 (5): 1887-1921.
Bohlmark, Anders, and Matthew J. Lindquist. 2006. “Life-Cycle Variations in the Association
between Current and Lifetime Income: Replication and Extension for Sweden.” Journal of
Labor Economics, 24 (4): 879-900.
Card, David, and Alan B. Krueger. 1992. “Does School Quality Matter? Returns to Education and
the Characteristics of Public Schools in the United States.” Quarterly Journal of Economics,
100 (1): 1-40.
Chetty, Raj, and Nathalien Hendren. 2015. “The Impacts of Neighborhoods on Intergenerational
Mobility: Childhood Exposure Effects and County-Level Estimates.” Harvard University,
mimeo.
Chetty, Raj, Nathalien Hendren, and Lawrence F. Katz. 2016. “The Effects of Exposure to Better
Neighborhoods on Children: New Evidence from the Moving to Opportunity Experiment.”
American Economic Review, 106(4): 855-902.
Chetty, Raj, John N, Friedman, Nathaniel Hilger, Emmanuel Saez, Diane Whitmore
Schanzenbach, and Danny Yagan. 2011. “How Does Your Kindergarten Classroom Affect
Your Earnings? Evidence from Project STAR.” Quarterly Journal of Economics, 126 (4):
1593-660.
Dearden, Lorraine, Javier Ferri, and Costas Meghir. “The Effect of School Quality on Educational
Attainment and Wages.” 2002. Review of Economics and Statistics, 84: 1-20.
Falch, T., B. Strom, and A.M.J. Sandsor (2015), “Do Smaller Classes Always Improve Students’
Long Run Outcomes?” Norwegian University of Science and Technology Working Paper 3.
40
Francesconi, Marco, and James J. Heckman. 2016. “Symposium on Child Development and
Parental Investment: Introduction.” Institute for the Study of Labor Discussion Paper No.
9977.
Fredriksson, Peter, Björn Öckert, and Hessel Oosterbeek. 2013. “Long-Term Effects of Class
Size.” Quarterly Journal of Economics, 128 (1): 249-85.
Gibbons, Stephen, Olmo Silva, and Felix Weinhardt. 2013. “Everybody Needs Good Neighbours?
Evidence from Students’ Outcomes in England.” Economic Journal, 123: 831-74.
Gould, Eric D., Victor Lavy, and M. Daniele Paserman. 2011. “Sixty Years after the Magic Carpet
Ride: The Long-Run Effect of the Early Childhood Environment on Social and Economic
Outcomes.” Review of Economic Studies, 78: 938-73.
Haider, Steven J. 2001. “Earnings Instability and Earnings Inequality of Males in the United
States: 1967-1991.” Journal of Labor Economics, 19 (4): 799-836.
Haider, Steven J., and Gary Solon. 2006. “Life-Cycle Variation in the Association between
Current and Lifetime Earnings.” American Economic Review, 96 (4): 1308-20.
Hanushek, Erik A. 2006. “School Resources.” In Handbook of the Economics of Education,
Volume 2, ed. Eric A. Hanushek, and Finis Welch, 865-908. Amsterdam: Elsevier Science,
North Holland.
Jacob, Brian. 2004. “Public Housing, Housing Vouchers, and Student Achievement: Evidence
from Public Housing Demolitions in Chicago.” American Economic Review, 94 (1): 233-58.
Jenkins, Stephen J. 1987. “Snapshots vs. Movies: ‘Lifecycle biases’ and the Estimation of
Intergenerational Earnings Inheritance.” European Economic Review, 31 (5): 1149–58.
Landersø, Rasmus and James J. Heckman. 2016. “The Scandinavian Fantasy: The Sources of
Intergenerational Mobility in Denmark and the U.S.” Forthcoming, Scandinavian Journal of
Economics.
41
Leuven, Edwin and Sturla A. Løkken. 2015. “Long Term Impacts of Class Size in Compulsory
Schooling.” University of Oslo mimeo.
Ludwig, Jens, Greg J. Duncan, Lisa A. Gennetian, Lawrence F. Katz, Ronald C. Kessler, Jefrey R.
Kling, and Lisa Sanbonmatsu. 2013. “Long-term Neighborhood Effects on Low-Income
Families: Evidence from Moving to Opportunity.” American Economic Review: Papers &
Proceedings, 103 (3): 226–31.
Mincer, Jacob. 1958. “Investment in Human Capital and Personal Income Distribution” Journal of
Political Economy, 66 (4): 281-302.
Nybom, Martin, and Jan Stuhler. 2016. “Heterogeneous Income Profiles and Life-Cycle Bias in
Intergenerational Mobility Estimation.” Journal of Human Resources, 51 (1): 239-68.
Oreopoulos, Philip. 2003. “The Long-Run Consequences of Living in a Poor Neighborhood.”
Quarterly Journal of Economics, 118 (4): 1533-75.
Page, Marianne, and Gary Solon. 2003. “Correlations between Brothers and Neighboring Boys in
their Adult Earnings: The Importance of Being Urban.” Journal of Labor Economics, 21 (4):
831-56.
Carsten Bøcker Pedersen, Heine Gøtzsche, Jørgen Østrup Møller and Preben Bo Mortensen. 2006.
“The Danish Civil Registration System. A cohort of eight million persons.” Danish Medical
Bulletin, 53 (4): 441-9.
Raaum, Oddbjrön, Erik Sörensen, and Kjell G. Salvanes 2006. “The Neighbourhood Is Not What
It Used to Be.” Economic Journal, 116 (1): 200-22.
Solon, Gary. 1999. “Intergenerational Mobility in the Labor Market.” In Handbook of Labor
Economics, Vol. 3A, ed. Orley Ashenfelter, and David Card, 1761-1800. Amsterdam:
Elsevier Science, North Holland.
Wilson, William J. 1987. “The Truly Disadvantaged.” Chicago: Chicago University Press.
42
Table 1
Cohorts included in the sample
(1) (2) (3) (4) (5) (6) (7) (8)
Birth First year # years Last age Earnings Persons School Parish
cohorts observed observed observed Observations cohorts cohorts
1960-61 1984 28 51 1,468,021 61,366 2,402 3,762
1962-63 1986 26 49 1,438,443 64,167 2,514 3,950
1964-65 1988 24 47 1,432,075 68,440 2,724 4,081
1966-67 1990 22 45 1,326,020 69,213 2,873 4,078
1968-69 1992 20 43 1,077,084 61,503 2,896 4,052
1970-71 1994 18 41 981,639 61,724 2,933 4,033
1972-73 1996 16 39 879,885 61,720 2,964 4,005
1974-75 1998 14 37 749,119 59,731 2,958 3,991
1976-77 2000 12 35 579,591 53,530 2,909 3,958
1978-79 2002 10 33 452,792 49,850 2,903 3,954
1980-81 2004 8 31 327,221 44,426 2,913 3,900
1982-83 2006 6 29 227,969 40,320 2,918 3,858 1960-83 1984-2006 6-28 29-51 10,930,859 695,960 33,907 47,622
The table reports sample characteristics by birth cohort for men born 1960-1983. Schools are defined using school of enrollment at age 15; neighborhoods are defined using the parish of residence at age 15. Column 7 reports the number of year-of-birth-by-school clusters within each birth cohort; Column 8 reports the number of year-of-birth-by-parish clusters within each birth cohort.
43
Table 2
Neighborhood and long run earnings – key study characteristics. (1) (2) (3) (4)
Page and Solon (2003)
Raaum, et.al. (2006)
Oreopoulos (2003)
Our study
Location United States Norway Toronto, Canada Denmark
Neighborhood PSID cluster Census tract Housing project Parish
Proximity 20-30 dwellings 44 km2 20 buildings 20 km2
#Clusters 120 7,996 and 8,818 81 47,622
#Men observed 443 228,700 4,060 695,960
Men/cluster 4 14 50 15
Others/cluster 86 450 1,036 2,443
Exposures
Birth cohorts 1952-62 1946-65 1963-70 1960-84
Years 1968 1960 and 1970 1978-86 1975-99
Ages 6-16 5-15 8-16 15
Duration snapshot snapshot 1-9 years snapshot
Outcomes
Measure Earnings Residual earnings Income Residual earnings
Duration (years) 5 6 3 6-28 (mean 16)
Transformation total mean total mean total mean untransformed
Years observed 1987-91 1990-95 1997-99 1984-2011
Ages observed 25-39 25-50 27-36 24-51
44
Table 3
Parameter estimates of permanent earnings
Panel A - Shared components (heterogeneous income profile –random growth)
Coeff. s.e.
Variance of intercepts Family ()12& ) 0.1482 0.0241 School ()14& ) 0.0174 0.0083 Neighborhood ()15& ) 0.0203 0.0095
Variance of slopes Family ()32& ) 0.0026 0.0004 School ()34& ) 0.0002 0.0001 Neighborhood ()35& ) 0.0005 0.0002
Covariance intercepts-slopes
Family ()132) -0.0117 0.0020 School ()134) -0.0030 0.0009 Neighborhood ()135) -0.0053 0.0012
Covariance between components Family-School ()24) 0.0074 0.0034 Family-Neighborhood ()25) 0.0101 0.0039 School- Neighborhood ()45) 0.0050 0.0009
Panel B - Idiosyncratic components (restricted income profile-random walk)
Coef. s.e.
Initial condition (age 24) Brother 1 ()*&',�& ) 0.0822 0.0134 Brother2 ()*&',&& ) 0.0731 0.0129
Variance of innovations Brother 1 ().�& ) 0.0730 0.0127 Brother 2 ().&& ) 0.0593 0.0101 The table reports Equally-Weighted Minimum Distance estimates for the parameters of the permanent component of the earnings process. Panel A reports parameter estimates for the earnings components shared by siblings, whereas Panel B reports parameter estimates for sibling-specific components. Estimates are derived using 65,199 empirical variances and covariances.
45
Table 4
Parameter estimates of transitory earnings
Coeff. s.e.
Initial condition (age 24) Brother 1 ()&',�& ) 0.6385 0.0298 Brother 2 ()&',&& ) 0.6062 0.0293
Variance of innovations at 25 Brother 1 ()?�& ) 0.4786 0.0246 Brother 2 ()?&& ) 0.4655 0.0248
Age splines in variance of innovations Brother 1
26-28 -0.1595 0.0047 29-33 -0.1318 0.0035 34-38 0.0447 0.0060 39-43 0.0507 0.0045 44-51 0.0255 0.0041
Brother 2 26-28 -0.1575 0.0067 29-33 -0.1290 0.0057 34-38 0.0294 0.0084 39-43 0.0580 0.0084 44-51 0.0314 0.0117
Autoregressive coefficient
Brother 1 (=�) 0.4418 0.0035 Brother 2 (=&) 0.4511 0.0045
Cross-person associations in transitory earnings Sibling covariance of innovations ()�) 0.0009 0.0014 Peers covariance of transitory earnings (catch-all components)
Sharing both school and neighborhood (P��) -0.0010 0.0008 Sharing only school (P� ) 0.0019 0.0009 Sharing only neighborhood (P� ) -0.0010 0.0010
The table reports Equally-Weighted Minimum Distance estimates for the parameters of the permanent component of the earnings process. Estimates are derived using 65,199 empirical variances and covariances.
46
Table 5
Decomposition of average sibling correlation: baseline, ignoring sorting and robustness to identification
(1) (2) (3) (4) (5)
Baseline
Only Siblings
Without Siblings
Cohorts 1966-1983
Cohorts 1966-1983
Sharing Community
With only Movers
Corr. s.e.
Corr. s.e.
Corr. s.e.
Corr. s.e.
Corr. s.e.
Siblings 0.319 0.010
0.313 0.011
0.299 0.008
0.316 0.013
Family 0.298 0.012
0.268 0.011
0.272 0.011
0.271 0.013
Neighborhood (N)
0.010 0.010
0.015 0.001
0.026 0.001
0.004 0.011
0.011 0.012
School (S) 0.011 0.010
0.029 0.001
0.044 0.001
0.023 0.010
0.034 0.011
Community (N+S)
0.021 0.009 0.045 0.001 0.071 0.001 0.027 0.010 0.045 0.012
The table reports the predicted sibling correlation for the case of siblings sharing the community and its decomposition into family and community effects, for the main estimating sample in Column 1 and in various subsamples in Columns 2 to 5. Predictions are generated using the formulae provided in Section 2.4.
47
Table 6
Decomposition of average sibling correlation: robustness to sample selection and definition
of community
(1) (2) (3) (4) (5) Siblings Family Neighborhood School Community
Baseline 0.319 0.298 0.01 0.011 0.021
(0.010) (0.012) (0.010) (0.010) (0.009)
Up to 2 0.344 0.318 0.017 0.009 0.026
children (0.016) (0.021) (0.015) (0.012) (0.015)
Up to 3 0.296 0.286 0.020 -0.010 0.010
children (0.013) (0.016) (0.015) (0.012) (0.012)
Excluding 0.329 0.308 0.010 0.011 0.021
singletons (0.011) (0.013) (0.010) (0.009) (0.009)
Excluding private 0.311 0.291 0.005 0.015 0.020
schools (0.011) (0.013) (0.011) (0.010) (0.010)
Peers at 14 and 15 0.319 0.299 0.011 0.009 0.021
(0.010) (0.012) (0.010) (0.009) (0.009)
Main parish of 0.319 0.300 0.006 0.013 0.019
residence 14-18 (0.011) (0.013) (0.010) (0.009) (0.009)
ZIP codes 0.322 0.313 -0.015 0.024 0.008
(0.011) (0.014) (0.012) (0.010) (0.010) The table reports the predicted sibling correlation for the case of siblings sharing the community and its decomposition into family and community effects, providing a sensitivity analysis of the main decomposition to various sample selections and community definitions. Predictions are generated using the formulae provided in Section 2.4. Standard errors in parentheses.
48
Table 7
Decomposition of average sibling correlation: robustness to age used to define
neighborhoods
(1) (2) (3) (4) (5) Siblings Family Neighborhood School Community Baseline on cohorts 0.299 0.272 0.004 0.023 0.027
1966-1983 (0.008) (0.011) (0.011) (0.010) (0.010) Parental parish 0.329 0.307 0.004 0.018 0.022
when 15 (0.012) (0.016) (0.013) (0.012) (0.013) Parental parish 0.356 0.325 0.011 0.020 0.031
when 14 (0.016) (0.019) (0.013) (0.012) (0.014) Parental parish 0.356 0.325 0.011 0.020 0.030
when 13 (0.016) (0.019) (0.013) (0.012) (0.014) Parental parish 0.349 0.312 0.019 0.018 0.037
when 12 (0.015) (0.018) (0.011) (0.011) (0.013) Parental parish 0.289 0.261 0.011 0.017 0.028
when 11 (0.009) (0.015) (0.012) (0.012) (0.015) Parental parish 0.294 0.267 0.009 0.018 0.028
when 10 (0.010) (0.015) (0.013) (0.012) (0.015) The table reports the predicted sibling correlation for the case of siblings sharing the community and its decomposition into family and community effects, providing a sensitivity analysis of the main decomposition to the age used to define neighborhoods. Predictions are generated using the formulae provided in Section 2.4. Standard errors in parentheses.
49
Figure 1
Sibling correlation of annual earnings
The figure shows raw sibling correlations of earnings over the life cycle. The line labelled “At same age” is obtained by computing the sibling correlation when the brothers are at the same point in their life cycle, while the line labelled “Age of older brother fixed at 35” is obtained by computing the sibling correlation when the older brother is 35.
50
Figure 2
Sibling correlation of annual earnings by siblings’ age gap
The figure shows raw sibling correlations of earnings over the life cycle. The lines are obtained by computing the sibling correlation when the brothers are at the same point in their life cycle, and refer to sibling pairs with an age gap of 5, 8 and 10 years.
51
Figure 3
Correlation of annual earnings for members of youth communities
The figure shows raw correlations of earnings for non-sibling peers over the life cycle. Schoolmates are defined as individuals attending the same school at age 15. Neighbors are defined as individuals residing in the same parish at age 15. Unrelated are defined as individuals sharing neither the family nor the school at age 15; in this case correlations are computed after generating 1000 random matches from the sub-population satisfying that definition.
52
Figure 4
Predicted sibling correlation of permanent earnings and factor decomposition
The figure shows the predicted sibling correlation over the life cycle for the case of siblings sharing the community and its decomposition into family and community effects. Predictions are generated using the formulae provided in Section 2.4.
0
.2
.4
.6
25 30 35 40 45 50Age
Sibling Family
School Neighborhood
53
Figure 5
Predicted sibling correlation of permanent earnings and factor decomposition: full sample vs. sample of movers
Cohorts ≥ 1966, Full Sample Cohorts ≥ 1966, Only Movers
The figure shows the predicted sibling correlation over the life cycle for the case of siblings sharing the community and its decomposition into family and community effects. Predictions are generated using the formulae provided in Section 2.4. Predictions are obtained for the full sample of cohorts born 1966 or later (left panel), or for the subsample among those cohorts whose family moved parish after the older brother turned 10 (right panel).
54
Appendix A Moment restrictions for transitory earnings
Considering two non-necessarily different age levels � and �F , the intertemporal covariance
structure of the transitory component of individual earnings from the birth order specific AR(1)
process is as follows:
�����������G� = [Z(� = �F = 24)D�)&'-& +
Z(� = �F > 24)� exp�C-(�)� + �]�<����(���)�=-&� + (A.1)
Z(� ≠ �F)� �<����(���)<�����G�=-�];�;�G .
Allowing for correlation of AR(1) innovations across brothers, the model yields restrictions
on transitory earnings also for cross-brothers moments:
o������G��G�G�Gp =
)� qr1 − o=�=&R���GRpst 1 − =�=&|���G| uv��w�G�
qr1 − o=&=�R���GRpst 1 − =&=�|���G| uv��x�G�
;�;�G ; ∀ I, IF, J, JF, (A.2)
where P is the number of overlapping years the two brothers are observed in the data.
We also model the correlation of transitory earnings across non-sibling peers. Differently
from the case of brothers, we do not model the correlation of AR(1) innovations among peers
because it would require distinguishing idiosyncratic components of transitory earnings for each
member of school or neighborhood clusters, generating dimensionality issues. We, therefore,
collapse all the cross-peers covariance structure of the transitory component into catch-all “mass
point” factors absorbing all the parameters of the underlying stochastic process. For any two non-
necessarily different age levels � and �F , covariances of transitory earnings across non-sibling
peers are as follows:
������ , �G�G���G� = P���QR���GR;�;�G
������ , �G�G��G�G� = P��QR���GR;�;�G ∀ J ≠ JF (A.3)
55
������ , �G�G�G��G� = P��QR���GR;�;�G ∀ I ≠ IF.
The moment restrictions above characterize the inter-temporal distribution of transitory earnings
for each individual and between siblings and peers. The orthogonality assumption between
permanent and transitory earnings in equation (1) implies that moment restrictions of the full
model are the sum of moment restrictions for permanent and transitory earnings, the former being
discussed in Section 2.3 of the paper. In general, these restrictions are a non-linear function of a
parameter vector y . We estimate y by Minimum Distance (see Chamberlain, 1984; Haider,
2001). We use Equally-Weighted Minimum Distance (EWMD) and a robust variance estimator
z�](y) = ({′{)��{′z{({′{)��, where z is the fourth moments matrix and { is the gradient
matrix evaluated at the solution of the minimization problem.
56
Table A1: Parameter estimates of time effects (1984=1)
Permanent Component (��)
Transitory Component (;�) Coeff. s.e.
Coeff. s.e.
t=
1985 0.9038 0.0712 0.9666 0.0255 1986 0.8603 0.0700 0.9769 0.0258 1987 0.8695 0.0725 0.9699 0.0292 1988 0.8500 0.0705 1.0053 0.0281 1989 0.8395 0.0707 1.0463 0.0313 1990 0.8479 0.0700 1.0680 0.0300 1991 0.8736 0.0713 1.0505 0.0326 1992 0.7734 0.0628 1.1302 0.0346 1993 0.7512 0.0615 1.1441 0.0348 1994 0.7178 0.0586 1.1453 0.0353 1995 0.6622 0.0545 1.0580 0.0330 1996 0.6406 0.0524 1.0678 0.0337 1997 0.5888 0.0482 1.0533 0.0317 1998 0.5636 0.0461 1.0386 0.0325 1999 0.5342 0.0440 1.0665 0.0321 2000 0.5115 0.0424 1.0972 0.0335 2001 0.4779 0.0398 1.1174 0.0326 2002 0.4643 0.0390 1.1588 0.0341 2003 0.4558 0.0384 1.1859 0.0349 2004 0.4230 0.0358 1.1488 0.0350 2005 0.3917 0.0333 1.1061 0.0337 2006 0.3481 0.0297 1.0931 0.0338 2007 0.3147 0.0269 1.0610 0.0329 2008 0.2914 0.0252 1.0676 0.0345 2009 0.2896 0.0250 1.1795 0.0386 2010 0.2764 0.0239 1.2178 0.0410 2011 0.2667 0.0232 1.1668 0.0401
The table reports Equally-Weighted Minimum Distance estimates for the time shifters. Estimates are derived using 65,199 empirical variances and covariances.
57
Table A2: Parameter estimates of cohort effects (1966-67=1)
Permanent Component (��)
Transitory Component (D�) Coeff. s.e.
Coeff. s.e.
c=
1960-61 0.7380 0.0218 1 1962-63 0.8253 0.0208 1 1964-65 0.9457 0.0216 1 1968-69 1.1437 0.0305 1.0041 0.0399 1970-71 1.3462 0.0361 0.9208 0.0383 1972-73 1.5193 0.0408 0.9118 0.0418 1974-75 1.6202 0.0494 1.0180 0.0474 1976-77 1.8552 0.0622 0.9538 0.0454 1978-79 2.2424 0.0793 0.8450 0.0426 1980-81 2.5622 0.1052 0.8693 0.0497 1982-83 2.801 0.1486 0.9127 0.0579
The table reports Equally-Weighted Minimum Distance estimates for the time shifters. Estimates are derived using 65,199 empirical variances and covariances.
top related